For one week management determined the number of units produced at the end of t hours during an eight-hour shift. The average values of x for the week are shown in the table.

Question

The cost of producing x units of a product is C = 60x + 1350. For one week management determined the number of units produced at the end of t hours during an eight-hour shift. The average values of x for the week are shown in the table.

t	0	1	2	3	4	5	6	7	8
x	0	16	56	130	200	269	339	386	391

(a) Use a graphing utility to fit a cubic model to the data. (Round your coefficients to three decimal places.)

x(t)=?

(b) Use the Chain Rule to find dC/dt. (Round your coefficients to three decimal places.)

dC/dT=?



Answer 1

(a)

Using Desmos to fit the data to a cubic model,

x=f(t) = at³+bt²+ct+d

Desmos will give you the values of a,b,c and d, which you need to round to three decimal places for each.

(b)

C(t) = 60x+1350 = 60f(t)+1350

C'(t) = 60 dx/dt = 60(3at²+2bt+c) = 180at²+120bt+60c

All that's left is the arithmetic.